Teachers’ Involvement in Designing MERLO Items: Boundary Crossing

Abstract

Meaning Equivalence Reusable Learning Objects (MERLO) items are a new kind of didactical tool that can be designed by teachers and used in classes, in tasks aimed at engaging students in deep reasoning, exploring and arguing about mathematical concepts. The interactions across communities of mathematics teachers and educators in on-line professional development were studied with attention to the phenomenon of boundary crossing of MERLO items, viewed as boundary objects in this article. The study analyseda first (international) crossing of the object that passedinstitutional boundaries (between Australian and Italian school systems), and a second crossing of the same object –inside the Australian institutional community – that passed boundaries (from static to dynamic representations) that we interpret in terms of method both for teachers and for researchers. This passage is possible due to the use of dynamic geometry software (GeoGebra) that supported a modification in the design of the item. The analysis shows boundary crossing as a process of transformation that can influence a modification (more or less stable) in the practices of the teachers involved and provides a deep research insight in relation to existing theoretical frameworks.

Effective communication of learning intentions and success criteria in the mathematics classroom: MERLO pedagogy for Senior Phase South African schools

“…Since the 1990s, MERLO has been a pedagogy and teaching technique developed, validated and experimented with within different countries and across different content areas and disciplines (Etkind, Shafrir, Kenett, & Roytman, 2016;Etkind & Shafrir, 2013;Etkind et al, 2010). As a pedagogical tool, MERLO is appropriate for different versions of core content based on sharing the meaning across different forms of representation (Arzarello et al, 2015;Robutti et al, 2016, 2020a, Robutti, Prodromou, & Aldon, 2020b. Additionally, MERLO is a powerful tool for problem-solving mathematical concepts known as duplication obstacles, extensive in all mathematics classrooms.…”

“…Scholars have demonstrated that designing MERLO patterns requires some steps to acquire different equivalence forms of representations that share the same mathematical meaning with the TS (Arzarello et al, 2015;Prodromou, 2015;Robutti et al, 2016Robutti et al, , 2020aRobutti et al, , 2020b. According to Arzarello et al (2015) and Prodromou (2015), the basis for designing MERLO items is to identify a close link that relates to the concept because it needs a change from old-style questions into present-day questions.…”

“…Furthermore, the TS was designated as an open question because 'teachers acquired the practice of elaborating the TS (i.e., TS) as a statement, graph, or table' (Arzarello et al, 2015, p. 5). Several studies have indicated that in designing MERLO items, there are some difficulties in choosing items that share the same mathematical meaning with the TS (Robutti et al, 2016(Robutti et al, , 2020a(Robutti et al, , 2020b. This implies that teachers must choose representation items that are linked with one another before designing MERLO activities.…”

“…To design and prepare the statement for Q4 is different because it does not have the equivalence of meaning and surface similarity to the TS and Q2. These characteristics imply that Q4 does not share the same meaning as the TS and does not appear to be the same as the TS (Robutti et al, 2016(Robutti et al, , 2020a(Robutti et al, , 2020b.…”

“…Teachers explained the terminologies associated with MERLO, such as TS, surface similarity, meaning equivalence and quadrants (Arzarello et al, 2015;Prodromou, 2015;Robutti et al, 2016Robutti et al, , 2020aRobutti et al, , 2020b.…”